Space and Time Invariance (Classical Wave Equation)

[mess1n]

Hey, I've come across a part in my notes which I can't figure out. Essentially it says:

$$\frac{\partial^{2}y}{\partial t^{2}}$$ = v$$^{2}$$ . $$\frac{\partial^{2}y}{\partial x^{2}}$$ is space and time invariant.

Whereas:

$$\frac{\partial y}{\partial t}$$ = -v . $$\frac{\partial y}{\partial x}$$ is not.

Why is this the case?

Cheers,
Andrew

 

[Antiphon]

Try putting a simple wave like y(x,t) = sin(x+vt) into both equations and see what happens.

Guessing at equations is a standard way for physicists to explore a problem.